Roller coaster: kinetic energy

In summary: Thats very simple and straight forward. use the conservation of energy law, and solve for the unkwon K=kinetic energy at the top of the loop. NB: th energy at initial position is equal to the energy at final position = top of the loop. initial kinetic energy = 0, So u will left only with final unknown kinetic energy K. Min Velocity, v=gR^0.5any probs rplying please?
  • #1
jaded18
150
0
A roller coaster car may be approximated by a block of mass m. The car, which starts from rest, is released at a height h above the ground and slides along a frictionless track. The car encounters a loop of radius R, as shown. Assume that the initial height h is great enough so that the car never loses contact with the track.

http://session.masteringphysics.com/problemAsset/1011023/13/MPE_ug_2.jpg

so, i know kinetic energy = .5m(v^2) and centripetal force in circle is m(v^2)/R so that if i play around with the equations i can get KE = 0.5m(gR) ... but how do i take into account the height if i have to give my answer in terms of m, g, h, and R?

Anyone out there who can solve this thing?
 
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  • #2
Find an expression for the kinetic energy of the car at the top of the loop.
Express the kinetic energy in terms of m, g, h, and R.

forgot to add that what's above is the problem!
 
  • #3
Just use conservation of energy... I don't think you need to deal with centripetal motion or anything.
 
  • #4
i can't work just on that. what do you mean by 'just use conservation of energy'. i need to express my answer in terms of those variables i listed above.
 
  • #5
jaded18 said:
i can't work just on that. what do you mean by 'just use conservation of energy'. i need to express my answer in terms of those variables i listed above.

What is the energy of the coaster at the beginning when it's at rest? Take the gravitational potential energy on the ground to be 0.
 
  • #6
The energy of the coaster at the beginning is potential energy which is just mgh.
 
  • #7
jaded18 said:
The energy of the coaster at the beginning is potential energy which is just mgh.

Yes, now at the top of the loop, it has potential energy mg(2R), and kinetic energy. can you use conservation of energy to solve for kinetic energy?
 
  • #8
thanks! i got it ... now what if i want to find the minimum initial height h at which the car can be released that still allows the car to stay in contact with the track at the top of the loop? how would i approach this one?
 
  • #9
jaded18 said:
thanks! i got it ... now what if i want to find the minimum initial height h at which the car can be released that still allows the car to stay in contact with the track at the top of the loop? how would i approach this one?

Now you'd use the centripetal acceleration... what does the velocity need to be at the top of the loop for the car to maintain contact?
 
  • #10
well acceleration is V^2/R . and so min velocity would be v = gR ...
 
  • #11
sorry, v = (gr)^(1/2)
 
  • #12
jaded18 said:
sorry, v = (gr)^(1/2)

yup. so what is the total energy of the coaster when it is at the top of the loop? It has that same energy when it is released from rest.
 
  • #13
mgh... sorry I'm not getting it
 
  • #14
i set mgh-mg2R = 0.5(mv^2) and plugged in what i got for v ... so i ended up with h=3R but i think I'm off by some multiplicative factor ?

the ans should be in terms of R by the way...
 
  • #15
jaded18 said:
i set mgh-mg2R = 0.5(mv^2) and plugged in what i got for v ... so i ended up with h=3R but i think I'm off by some multiplicative factor ?

the ans should be in terms of R by the way...

can you show how you get h = 3R, I'm getting h = 2.5R
 
  • #16
ah, stupid calc. error. thanks lots learningphysics. you made my day haha
 
  • #17
jaded18 said:
ah, stupid calc. error. thanks lots learningphysics. you made my day haha

no prob.
 
  • #18
Thats very simple and straight forward. use the conservation of energy law, and solve for the unkwon K=kinetic energy at the top of the loop. NB: th energy at initial position is equal to the energy at final position = top of the loop. initial kinetic energy = 0, So u will left only with final unknown kinetic energy K. Min Velocity, v=gR^0.5
 
  • #19
any probs rply
 

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass of the object and its velocity.

How is kinetic energy related to roller coasters?

Roller coasters rely on kinetic energy to move along the track and provide riders with a thrilling experience. The potential energy at the top of the first hill is converted into kinetic energy as the roller coaster descends, and this energy is conserved throughout the ride.

What factors affect the amount of kinetic energy in a roller coaster?

The main factors that affect the amount of kinetic energy in a roller coaster are the mass of the roller coaster cars and the speed at which they are traveling. Heavier cars and higher speeds result in greater amounts of kinetic energy.

How does kinetic energy impact the safety of roller coasters?

The kinetic energy of a roller coaster is a crucial factor in ensuring the safety of riders. Designers must carefully calculate the maximum speed and height of a roller coaster to ensure that the kinetic energy remains within safe limits for both riders and the structure of the ride.

Can kinetic energy be converted into other forms of energy on a roller coaster?

Yes, kinetic energy can be converted into other forms of energy on a roller coaster. For example, friction between the wheels and the track converts some of the kinetic energy into thermal energy, and brakes can be used to convert the kinetic energy into potential energy for the next hill or into heat energy through friction.

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